That’s really interesting, and certainly puts the cat among the pigeons. I suspect that (a) this is getting beyond the reach of amateurs on a Welsh forum, in that we probably need searchable historical corpora of all the relevant languages and enough knowledge of the same to make sense of what we find; (b) potentially beyond anybody, in that I doubt all those corpora even exist; and © increasingly off-topic for Welsh!
For what it’s worth, I tried looking for some more Old English examples and came up with another construction similar to the Dutch one: in a description of Norway in Old English it mentions Finns who camped in various places on huntoðe on wintra ond on sumera on fiscaþe be þǣre sǣ (‘hunting in winter and fishing by the sea in summer’ – huntoð and fiscaþ are both nouns made from the verb-roots). Although I’ve translated that with an ‘-ing’ I don’t feel it’s really a continuous sense, more just naming the activity – much as being ‘at work’ isn’t necessarily quite the same as ‘working’! 
The version with the present participle seems to be quite old in Germanic, in that something like it comes up occasionally in Gothic when they’re trying to render subtleties of Greek tenses that Gothic didn’t really do (I’m thinking of was-uh þan Iohannes daupjands ana auþidai ‘and John was baptizing in the wilderness’), but that’s quite different from both the Welsh and the Dutch, even though it sounds like the modern English.
I’m still tempted to see Welsh influence on the English, because the structure seems to become used in Middle Welsh before it is completely adopted in English, but that doesn’t account for your Dutch example. Seeing them as part of a Sprachbund where they’re all doing similar things syntactically but each in their own words doesn’t really satisfy me, either, since from that point of view you’d think Dutch, along with English, mostly has the same kind of syntax and word-order that’s common to European languages (including Romance ones), and from which all the Celtic languages are really quite distinct.
On the whole I think I’m a-going to stick with “English not totally unlike Welsh for once” and give up on the reasons why…